In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application these properties become helpful in extension Pochhammer’s type contour integral representations Rodrigues formulae known hypergeometric functions. On point view, relations are discussed which useful interpreting the phenomenon spread infectious diseases terms Lauricella’s multiple

The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It shown that the derivative integral operators are bounded. Some fundamental characteristics of new operators, such as semi-group inverse characteristics, studied. As special cases these novel several already well known in literature acquired. generalized Laplace transform evaluated. By ...

This paper is involved with synchronization of fractional order stochastic systems in finite dimensional space, and we have tested its time response chaotic behaviors. Firstly, give a representation solution for system. Secondly, some useful sufficient conditions are investigated by using matrix type Mittag-Leffler function, Jacobian via process, stability analysis feedback control technique to...

The objective of this research is to obtain some fractional integral formulas concerning products the generalized Mittag–Leffler function and two H-functions. resulting are described in terms H-function several variables. Moreover, we give illustrative examples for efficiency general approach our results.

It has been shown that anomalous relaxation in dielectrics can be described in terms of equations with fractional derivatives. The solutions of the resulting equation with fractional derivatives are expressed by the Mittag –Leffler function and the Fox function. The conditions of a change from the Debye relaxation to “slow” (anomalous) relaxation with a power time dependence have been examined ...

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, P.R. China Abstract In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guaran...

In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate and the second one time-degenerate equation. Solutions to both are expressed series expansions. For problem, obtained solutions form of Fourier-Legendre series. Convergence uniqueness have been discussed. Fou...